Answer the following questions for a random graph generated by the Erdos-Renyi random graph model ER(n, p). You do not need to prove your answers are correct but still need to show your work. Your answer should be in terms of n and p. 8(a) What is the expected number of triangles? 8(b) What is the probability that d(u, v) > 2 for two particular vertices u v? (Hint: First, find the probability that d(u, v) > 1. Then consider, for all other vertices x, the probability that uxv is NOT a path in the random graph. Multiply all these probabilities together.) Note that for this question, no graph is given. However, we know that the expected number of edges for ER(n, p) random graph model is , and that the expected degrees of the vertex for the random graph model ER(n, p) is (n-1) *p
Answer the following questions for a random graph generated by the Erdos-Renyi random graph model ER(n, p). You do not need to prove your answers are correct but still need to show your work. Your answer should be in terms of n and p. 8(a) What is the expected number of triangles? 8(b) What is the probability that d(u, v) > 2 for two particular vertices u v? (Hint: First, find the probability that d(u, v) > 1. Then consider, for all other vertices x, the probability that uxv is NOT a path in the random graph. Multiply all these probabilities together.) Note that for this question, no graph is given. However, we know that the expected number of edges for ER(n, p) random graph model is , and that the expected degrees of the vertex for the random graph model ER(n, p) is (n-1) *p
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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8. Answer the following questions for a random graph generated by the Erdos-Renyi random graph model ER(n, p). You do not need to prove your answers are correct but still need to show your work. Your answer should be in terms of n and p.
8(a) What is the expected number of triangles?
8(b) What is the probability that d(u, v) > 2 for two particular vertices u v? (Hint: First, find the probability that d(u, v) > 1. Then consider, for all other vertices x, the probability that uxv is NOT a path in the random graph. Multiply all these probabilities together.)
Note that for this question, no graph is given. However, we know that the expected number of edges for ER(n, p) random graph model is , and that the expected degrees of the vertex for the random graph model ER(n, p) is (n-1) *p
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